.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/oceanography/plot_08_ekman_dead_water.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_api_gallery_oceanography_plot_08_ekman_dead_water.py>`
        to download the full example code or to run this example in your browser via JupyterLite.

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_api_gallery_oceanography_plot_08_ekman_dead_water.py:


Ekman's dead water (1904)
=========================

On Nansen's Fram expedition the ship slowed to a crawl in fjords where a thin
layer of meltwater lay over salty sea water. Vagn Walfrid Ekman showed that
the ship was making waves on the hidden density jump. Those internal waves
travel at about ``sqrt(g' h)`` with the reduced gravity ``g' = g d_rho / rho``,
a few tens of centimetres per second, so a slow ship pours its energy into
them.

.. GENERATED FROM PYTHON SOURCE LINES 12-31



.. image-sg:: /api/gallery/oceanography/images/sphx_glr_plot_08_ekman_dead_water_001.png
   :alt: Waves on a hidden density jump
   :srcset: /api/gallery/oceanography/images/sphx_glr_plot_08_ekman_dead_water_001.png
   :class: sphx-glr-single-img





.. code-block:: Python


    import matplotlib.pyplot as plt
    import numpy as np

    from earthsciencekit.constants import GRAVITY
    from earthsciencekit.oceanography import internal_wave_speed, reduced_gravity, shallow_wave_speed

    upper = np.linspace(0.5, 10, 200)
    fig, ax = plt.subplots()
    for contrast in [5, 10, 20]:
        gprime = reduced_gravity(contrast, 1025, GRAVITY)
        deep_limit = internal_wave_speed(gprime, upper, 1e6)
        np.testing.assert_allclose(deep_limit / shallow_wave_speed(upper, GRAVITY), np.sqrt(contrast / 1025), rtol=1e-5)
        ax.plot(upper, internal_wave_speed(gprime, upper, 100), label=f"density jump {contrast} kg/m^3")
    ax.axhspan(0.5, 0.8, color="tab:red", alpha=0.15, label="Fram in dead water")
    ax.set(xlabel="fresh-layer thickness [m]", ylabel="internal wave speed [m/s]", title="Waves on a hidden density jump")
    ax.legend()

    plt.show()


.. rst-class:: sphx-glr-timing

   **Total running time of the script:** (0 minutes 0.091 seconds)


.. _sphx_glr_download_api_gallery_oceanography_plot_08_ekman_dead_water.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

    .. container:: lite-badge

      .. image:: images/jupyterlite_badge_logo.svg
        :target: ../../../lite/lab/index.html?path=api/gallery/oceanography/plot_08_ekman_dead_water.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: plot_08_ekman_dead_water.ipynb <plot_08_ekman_dead_water.ipynb>`

    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: plot_08_ekman_dead_water.py <plot_08_ekman_dead_water.py>`

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: plot_08_ekman_dead_water.zip <plot_08_ekman_dead_water.zip>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_